This thesis investigates the feasibility of using spatial survival modelling techniques to
develop dynamic space-time predictive models of risk for infectious animal disease epidemics.
Examples of diseases with potentially vast socioeconomic impacts include avian
influenza, bovine tuberculosis and foot-and-mouth disease (FMD), all of which have received
wide coverage in the recent media. The relatively sporadic occurrence of such large
scale animal disease outbreaks makes determination of optimal control policies difficult,
and policy makers must balance the relative impacts of different response strategies based
on little prior information. It is in this situation that the use of mathematical and statistical
modelling techniques can provide powerful insights into the future course of an
infectious epidemic.
The motivating example for this thesis is the outbreak of FMD in Devon in 2001, however
we are interested in developing more general techniques that can be applied to other
animal diseases. Many of the models fitted to the 2001 UK FMD data set have focussed
on modelling the global spread of the disease across the entire country and then using
these models to assess the effects of nationwide response strategies. However it has been
shown that the dynamics of the disease are not uniform across the whole of the UK and
can vary significantly across different spatial regions. Of interest here is exploring whether
modelling at a smaller spatial scale can provide more useful measures of risk and guide
the development of more efficient control policies.
We begin by introducing some of the main epidemiological issues and concepts involved
in modelling infectious animal diseases, from the microscopic through to the farm population
level. We then discuss the various mathematical modelling techniques that have
applied previously and how they relate to various biological principals discussed in the
earlier chapters. We then highlight some limitations with these approaches and offer potential
ways in which survival analysis techniques could be used to overcome some of these
problems.
To this end we formulate a spatial survival model and fit it to the Devon data set with
some naive initial covariates that fail to capture the dynamics of the disease. Some work
by colleagues at the Veterinary Laboratories Agency, Weybridge (Arnold 2005), produced
estimates of viral excretion rates for infected herds of different species type over time,
and these form the basis for the development of a dynamic space-time varying viral load
covariate that quantifies the viral load acting at any spatial location at any point in time.
The novel use of this covariate as a means of censoring the data set via exposure is then
introduced, though the models still fail to explain the variation in the epidemic process.
Two potential reasons for this are identified - the possible presence of non-localised infections
and/or premise varying susceptibility. We then explore ways in which the survival
approach can be extended to model more than one epidemic process through the use of
mixture and long-term survivor models. Some simple simulations suggest that resistance
to infection is the most likely cause of the poor model fits, and a series of more complex
simulation experiments show that both the mixture and long-term survivor models offer
various advantages over the conventional approach when resistance is present in the data
set. However key to their performance is the ability to correctly capture the mixing, although
in the worst case scenario they still replicate the results from the conventional
model.
We also use these simulations to explore potential ways in which space-time predictions
of the hazard of infection can be used as a means of targeting control policies to areas of
‘high-risk’ of infection. This shows the importance of ensuring that the scale of the control
order matches the scale of the epidemic, and suggests possible dangers when using global
level models to derive response strategies for situations where the dynamics of the disease
change at smaller spatial scales. Finally we apply these techniques to the Devon data set
and offer some conclusions and future work.